Faster-than-light neutrinos face time trial
nature.com
nature.com
Whether it pans out or not, that's a nice eye for details. Props to the people who found it, it's at least something.
Isn't it the other way around? Gran Sasso site lies closer to the center of Earth and that's why it has bigger gravitational pull
However, unless I've totally forgotten what little I ever knew about GR, what matters for clocks is the gravitational potential, in such a way that clocks run slower in lower potentials. And the potential is definitely the lowest at the center of the Earth. Otherwise clocks would run the slowest far out in intergalactic space where there's practically no gravity, but that's not the case.
Let the radius of the Earth be R. Suppose that you are somewhere between the center of the Earth and the Earth's surface, say at x meters from the center. Then you can divide the Earth into two pieces: one smaller ball of radius x below you, and a shell with inner radius x and outer radius R "above you".
If you are inside or at the inner surface of a spherical shell, then the gravity from all the atoms in the shell is pulling at you in all directions. Now it so happens that all these little pulls exactly cancel each other out. This can be shown with Gauss' law. [Does anybody know an intuitive proof of this?]
So effectively only the inner ball of radius x counts. Now the question is whether this ball has bigger or smaller gravity than standing on the Earth's surface. It's not completely clear that the gravity is smaller because the density of the smaller ball could be different. If we assume that the density of the Earth is roughly uniform however, then it is clear that the gravity inside the Earth is lower than on its surface.
The precise condition for the gravity being lower at height x is that x/R < a/b where a is the average density of the of the Earth and b is the average density of the inner ball.
As you see, gravity gets stronger up to a maximum in the outer core, because the core is much more dense.
But the issue here is not about spherical Earths at all. Earth deviates significantly from a spheroid and even an ellipsoid shape-wise and gravity-wise. Just saying "location X lies closer to the center of the earth and therefore experiences less gravity" is somewhat irrelevant here.
imagine rays through you position that form narrow cones to the closest and the farthest point of the shell - if you're 2 times closer to one side than to another, they'd cut 4 times less (proportional to distance squared) of the shell on the closer side than on the farthest.
The gravitational pull (reverse of the distance squared) per unit mass is 4 times stronger from the pieces on the closer side. Thus 4 times stronger pull per unit mass from 4 times less mass - the same.
(for complete mathematical correctness now make the cones infinitesimally narrow, slice the shell into infinitesimally thin shells and integrate over the 2 angles [pie x pie] to cover the surface of the shell and over the thickness of the shell to cover all the layers - each such infinitesimal would be 0 as described above and integrating 0 would produce 0 in this case. For a general Gauss law it is based on the same distance squared proportionality of the surface element size and reverse distance squared proportionality of the field gradient value (ie. it works only for such fields) )
I asked because the one thing that the media repeats is that there's a lot of neutrinos hitting us right now, so how do we know they're the ones we're looking for?
Also, is there a normal speed that neutrinos travel at? Can you catch one at rest?
There are craploads of neutrinos left over from the Big Bang (see http://en.wikipedia.org/wiki/Cosmic_neutrino_background) but they are very low energy and are impossible to detect. They are likely the closest you can find neutrinos at rest. How fast they go depends on their rest mass, which we only know to be small but nonzero.
Same here, AFAICT. They're using pion and kaon decay that produces muon neutrinos of known energies (in a range) travelling in a known direction. Solar neutrinos (http://en.wikipedia.org/wiki/Solar_neutrino) are created as electron neutrinos, though they flavour shift, they are mainly coming the direction of the sun and have differing energies to those created in the OPERA experiment via the CERN SPS.
I'd guess that you can cut out a lot of the background neutrino flux by running the proton capture (to generate the neutrinos) at around noon; I don't know if they time things to put the detector orthogonal to the local galactic plane but that would (to this layman) seem sensible too.
One thing that did strike me (lol?) was that the kaon/pion decay happens along a 1095m decay tube. As a sibling comment says they're not tracking individual neutrinos (you can't detect them twice) they're tracking a range of energy events (via the muon's created) at a range of positions along a 1km tube (via the muon trajectories presumably) and pairing them with a range of events at the other end such that they need to know the length of the transit over 730km to an accuracy of 20cm.
It's amazing stuff.
Edit: I should probably have said that of course they allow for the variances and the statistical nature and other systematic uncertainties, the graph showing the calculated uncertainties can be seen on the Wikipedia page, http://en.wikipedia.org/wiki/CNGS.
>"The high-accuracy time-transfer GPS receiver allows to continuously monitor tiny movements of the Earth’s crust, such as continental drift that shows up as a smooth variation of less than 1 cm/year, and the detection of slightly larger effects due to earthquakes. The April 2009 earthquake in the region of LNGS, in particular, produced a sudden displacement of about 7 cm, as seen in Fig. 7. All mentioned effects are within the accuracy of the baseline determination. Tidal effects are negligible as well." //
Now that's accuracy, allowing for movement of the Earth's crust in your experiment!
Wonder if this can be used for Earthquake prediction.
Calling half time and changing ends is a nice idea, but utterly impractical. Finding/building an alternative neutrino source and pointing it at the detector is (I think) the best approach to reproducibility, but it still leaves open the possibility of systematic errors in the detection mechanism causing the same issues. A different distance should give a different delay though, which would be one test.
Another might be to try and use photons as a reference/synchronisation mechanism, but that's hindered by the fact that everything is in underground caverns.
Yes it would probably cost millions for such a thing to be done if it's even possible.
Figuring out the appropriate clock corrections very, very carefully seems like a better approach...
I wonder how accurate the GPS synchronization is too. I'm wondering if it takes into account different atmospheric conditions and the index of refraction of radio waves in air.
how about just inside the fiber. How good is the ping between CERN and Gran Sasso ? :)
This probably wouldn't work, time dilation under gravity makes my head hurt!
"Contaldi admits"
"Contaldi already has some company"
I wish they'd stop this. It's not a fight between the OPERA team and the world. They're not trying to get people to accept their result. This is everybody collectively trying to figure out why the data came out this way, with the expected result that there's a mistake somewhere.
Contaldi pointed out what he thought it might be, OPERA is saying "we don't think that's it, here's why", not "you're wrong, our results are correct".
I don't think that's it! [see last line].
Surely they're saying "you're wrong, that's no why our results are incorrect"?
"We don't think that's it" is just the polite version of "you're wrong" is it not. Of course one can (and should where possible) counter with "no you're wrong, here's why".